The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  X  1  1  1  1  1  1  1
 0  X  0  0  0  0  0  0  0  0  X 2X 2X  X  X  X  0 2X  X 2X  X  0  X  0 2X  X  0 2X  X 2X 2X 2X  X  X  0 2X  0  0 2X  X 2X  0 2X 2X  X  X  X  0  X 2X  X 2X  X
 0  0  X  0  0  0  0  X 2X 2X 2X  0  0 2X  X 2X  X  0  X  X  0 2X 2X  0  X  X 2X  0  X  0 2X 2X 2X  X  0  X  X  0 2X  X 2X  X  0  X  0  0  X  X  0  0  X  X  X
 0  0  0  X  0  0  X 2X  0 2X  0  0 2X  X  X 2X  0  X  0 2X  0 2X 2X  0 2X  0  X 2X 2X  X  X  X 2X  0 2X 2X  0  X 2X  0  X  X 2X  X 2X  0  0 2X 2X  0  X  X  0
 0  0  0  0  X  0 2X 2X  X  0 2X 2X 2X  0 2X 2X  0 2X  X  0 2X 2X  0  X 2X  0 2X  X  0  X  0  X  0 2X 2X  0 2X  X  0  X 2X  X 2X  X  0 2X  0  X  0  0 2X 2X 2X
 0  0  0  0  0  X 2X 2X 2X 2X 2X 2X  X 2X  X  X 2X  X 2X 2X 2X 2X  0 2X  0  X  0  0 2X  X 2X  0 2X  X  X  0  0  0  X  X  0  0 2X  0  X  0  0  X  0  X 2X  0 2X

generates a code of length 53 over Z3[X]/(X^2) who´s minimum homogenous weight is 96.

Homogenous weight enumerator: w(x)=1x^0+164x^96+122x^99+54x^100+324x^103+176x^105+648x^106+68x^108+432x^109+90x^114+24x^117+44x^123+28x^126+10x^132+2x^150

The gray image is a linear code over GF(3) with n=159, k=7 and d=96.
This code was found by Heurico 1.16 in 14.2 seconds.